Asymptotically Flat Space-Times and its Hidden Recesses: An Enigma from GR

TL;DR

This paper explores how transforming standard asymptotically flat space-times into Newman-Unti coordinates reveals relations resembling classical mechanics and electromagnetism, but in an abstract complex manifold called H-Space, raising questions about physical interpretation.

Contribution

It demonstrates that well-known solutions in Einstein-Maxwell theory exhibit Newtonian-like relations in a special coordinate system within H-Space, a novel geometric perspective.

Findings

Relations mimic classical mechanics and Maxwell theory

Motion and radiation are described in H-Space, not physical space-time

Transformations reveal hidden structures in asymptotically flat solutions

Abstract

We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory - absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) Asymptotically Flat Space-Times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of NU (Newman-Unti) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-Space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-Space and its dual space H. 1